A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Application of an elastic-plastic model to the use of small specimen strength ratio for measuring fracture toughness

Data reported by Server and Wullaert correlating specimen strength ratio with fracture toughness were analyzed with the D-BCS-HSW model. This model is based on the Dugdale model, elaborated by Bilby, Cottrell and Swinden, and extended by Heald, Spink and Worthington. The data included instrumented precracked Charpy results on HSST plate 02, as well as static, intermediate, and dynamic tests of 1 — T compact and bend specimens of SA533B-1 steel. The model relates the fracture toughness to the crack length, specimen shape and size, applied failure stress and effective flow strength. The only parameter not provided by the data is the constraint factor, M, the ratio of the effective flow strength to the yield strength. The model was fitted to the data by non-linear least squares methods by which M was determined to be approx. 2.5 for the Charpy data, and from 2.1 to 2.6 for the other specimen data. The fit is considered to be reasonably good throughout the range from linear-elastic fracture mechanics through to plastic collapse. The result for the Charpy data is considered to be as good as that for the other specimens. The determination of only one parameter is needed to establish the relationship between specimen strength ratio and fracture toughness. This relationship then applies to the entire range of fracture regimes.     

Study of the relationship between fracture toughness (J IC) and bulge ductility

A theoretical model relating fracture toughness expressed as J _IC and bulge ductility {ie71-1} for a material exhibiting linear elastic behavior at low temperature and elastic-plastic behavior at higher temperatures is proposed. This model shows a variation of J _IC with {ie71-2} for linear elastic behavior and J _IC with {ie71-3} for elastic-plastic behavior. The model contains three constants to be determined experimentally for a given material, specimen geometry and testing conditions. A case study on 1045 steel in the temperature range ?60 to 25°C confirms the validity of the model. The experimental results help in determining the size of the fracture zone ahead of the crack as well as the mechanisms for crack blunting and crack growth.     

Using local out-of-plane compression (LOPC) to study the effects of residual stress on apparent fracture toughness

To study and understand the effects of residual stresses on fracture behaviour, it is necessary to introduce well characterised and reproducible residual stresses into laboratory fracture specimens. One technique capable of providing such residual stresses is local compression, where the local compression is applied to the sides of a test specimen. In this paper, the technique is used to create a residual stress field in compact tension, C(T), specimens. The specimens are used subsequently to study the effects of residual stress on fracture. Finite element studies show that significant changes to the distribution of the residual stresses occur when the position of the compression tools is changed relative to the crack tip. It is also revealed that both a single and double pair of compression tools can generate both tensile and compressive residual stresses in the vicinity of the crack tip depending upon the location of the tools relative to the crack tip. The impact of local compression is illustrated by experimental results from room temperature fracture tests performed on two aluminium alloys, Al2650 and Al2024. Tensile residual stresses, created by the application of a single pair of compression tools, reduced the initiation fracture toughness of Al2650 by about one half. The ductile tearing resistance of Al2024 decreases when a double pair of tools introduces tensile residual stresses. Conversely, the tearing resistance increases when compressive residual stresses are created through local compression.     

Essential work of fracture (w e) versus energy dissipation rate (J c) in plane stress ductile fracture

Two measures of fracture toughness have been investigated. The first is the Cotterell's essential work of fracture (w _e) which reflects the energy absorbed in the process of localized necking and decohesion occurring within the crack tip region. The second is the familiar critical energy dissipation rate associated with the onset of crack extension and commonly designated by J _c. Total of 48 fracture tests have been performed on thin aluminum double-edge-notched panels and thin compact tension specimens with varying crack size-to-ligament ratios. In a simple experimental procedure it has been established that both measures are equivalent, at least under the plane stress conditions, and that they both represent the fraction of energy which is transmitted through the plastic deformation field into the crack tip region. The ratio essential work of fracture/total work of fracture has been suggested as a quantitative measure of the energy transmission process. Certain predictions are made concerning variations of the energy transmission factor (ETF) during the stable phase of ductile fracture propagation.

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Résumé On étudie deux mesures de la ténacité à la rupture. La première est le travail essentiel de rupture de Cotterell (w _e) qui représente l'énergie absorbée au cours du processus de striction et de décohésion localiseés qui se produit dans la région de l'extrémité d'une fissure. La deuxième est la notion familière de vitesse critique de dissipation d'énergie associée au démarrage de l'extension d'une fissure, qui est couramment représentée par J _c. On a procédé à un total de 48 essais de rupture sur des panneaux minces d'aluminium présentant une double entaille de bord, et sur des éprouvettes minces de traction compactes présentant divers rapport de longueur de fissure sur longueurs de ligaments. Par une procédure expérimentale simple, on a établi que les deux mesures de la ténacité sont équivalentes, du moins en état plan de tension, et qu'elles représentent toutes deux la fraction d'énergie qui est transmise au travers du champ de déformation plastique dans la zone de l'extrémité de la fissure. On suggère comme mesure quantitative du processus de transmission d'énergie d'utiliser le rapport travail essentiel de rupture/travail total de rupture. Diverses prédictions sont faites en ce qui concerne les variations du facteur de transmission d'énergie au cours de la phase stable de propagation d'une rupture ductile.

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On leave from The University of Wisconsin-Milwaukee     

Temperature, moisture and mode-mixity effects on copper leadframe/EMC interfacial fracture toughness

A systematic investigation and characterization of the interfacial fracture toughness of the bi-material copper leadframe/epoxy molding compound is presented. Experiments and finite element simulations were used to investigate delamination and interfacial fracture toughness of the bi-material. Two dimensional simulations using virtual crack closure technique, virtual crack extension and J-integral proved to be computationally cheap and accurate to investigate and characterize the interfacial fracture toughness of bi-material structures. The effects of temperature, moisture diffusion and mode-mixity on the interfacial fracture toughness of the bi-material were considered. Testing temperature and moisture exposure significantly reduce the interfacial fracture toughness, and should be avoided if possible.     

The effects of volume percent and aspect ratio of carbon fiber on fracture toughness of reinforced aluminum matrix composites

Carbon fiber reinforced aluminum matrix composites are used as advanced materials in aerospace and electronic industries. In order to investigate role of aspect ratio of carbon fiber on fracture toughness of aluminum matrix composite, the composite was produced using stir casting. Al–8.5%Si–5%Mg selected as a matrix. The samples were prepared with three volume fractions (1, 2 and 3) and three aspect ratios (300, 500 and 800). Three-point bending test was performed on the specimens to evaluate the fracture toughness of the materials. The results showed that the fracture toughness of composites depends on both fiber volume fraction and aspect ratio. Scanning electron microscopy (SEM) was employed to elucidate the fracture behavior and crack deflection of composites. The study also, showed that the toughening mechanism depends strongly on fiber volume fraction, aspect ratio and the degree of wetting between fiber and matrix.     

Mechanisms for rate effects on interlaminar fracture toughness of carbon/epoxy and carbon/PEEK composites

The objective of this study was to investigate strain-rate dependent energy absorption mechanisms during interlaminar fracture of thermosetting (epoxy) and thermoplastic (PEEK) uni directional carbon fibre (CF) composites. A simple model addressing the translation of matrix toughness to mode I and mode II interlaminar toughness of the composite is presented, in conjunction with a fractographic examination of the fracture surfaces and the fracture process. The observed rate dependency of composite fracture toughness is attributed to the rate dependent toughness of the viscoelastic matrix and the size of the process zone around the crack tip. Other important factors identified are the roughness of the fracture surface and fibre bridging.     

A crack growth resistance curve approach to fiber/metal laminate fracture toughness evaluation

Fiber/metal laminates consist of thin, high strength aluminum alloy sheets alternately bonded to plies of fiber-reinforced epoxy adhesive. This new class of material combines the best features of organic matrix composites and metals. Tests conducted on wide centrally slotted panels show that fiber/metal laminates, like metals, exhibit capacity for slow stable tearing prior to rapid fracture. It is also shown that a fracture mechanics based R-curve approach, similar to that used for metals, can be applied to predict effects of size and geometry on slotted laminate panel residual strength. These results represent an important step in the development of analytical practices for fiber/metal laminate damage tolerance and airworthiness assessments.     

The effect of hygrothermal conditions on the fracture toughness of epoxy/poly(styrene-co-allylalcohol) blends

The influence of water content on the fracture toughness of epoxy/poly(styrene-co-allylalcohol) (PScoPA) blends with different amounts of modifier has been investigated. The water ingress has a double consequence: a considerable plasticization effect of the matrix and a significant weakening of the interphase between the matrix and the thermoplastic particles. The addition of thermoplastic modifier reduces, in the aged samples, the deterioration in fracture toughness. Analytical models, based on plastic voids growth around the dispersed phase particles, have been applied with reasonable agreement.     

A method to evaluate ductile fracture toughness based on load separation principle

In combination with load separation principle, the P‐V curves of blunt‐notched specimens with different stationary cracks can be explicitly expressed as a unified formula. Further, a load separation‐based direct calibration (LSDC) method to predict instantaneous crack size and J‐resistance curve of growing cracked specimen has been developed. Two specimen configurations, compact tension and single edge‐notched bending, which are made of Cr2Ni2MoV and Q345B, respectively, are employed to verify the validity of LSDC method. The results show that the estimated J‐resistance curves are more reasonable in comparison with those obtained by unloading compliance and normalization method.     

A data reduction method based on the J-integral to obtain the interlaminar fracture toughness in a mode II end-loaded split (ELS) test

Various difficulties arise in the data reduction of the end-loaded split (ELS) test. On one hand, a small Fracture Process Zone (FPZ) at the crack front is assumed in the existing mode II end-loaded split test methodologies based on Linear Elastic Fracture Mechanics (LEFM). However, mode II fracture has been reported to involve large FPZ and a fuzzy crack tip. Furthermore, the ELS test, is usually affected by geometrical non-linearities.This work proposes a closed-form solution based on the J-integral to determine the interlaminar fracture toughness in an ELS test. This solution avoids the need to measure the crack length, and is applicable when a large FPZ is present, as occurs in adhesive bonded joints between CFRP. In addition, because the ELS test involves large vertical deflections, a correction of the formulation for large displacements has been implemented.This new methodology has been compared to other methods available in the literature based on LEFM by means of an experimental campaign of delamination tests using unidirectional CFRP specimens in order to make a first validation of the method.     

Miscibility, morphology and fracture toughness of tetrafunctional epoxy resin/poly (styrene-co-acrylonitrile) blends

Poly(styrene-co-acrylonitrile) (SAN) was found to be miscible with the tetraglycidylether of 4,4'-diaminodiphenylmethane (TGDDM), as shown by the existence of a single glass transition temperature (T _g) over the whole composition range. However, SAN was found to be immiscible with the 4,4-diaminodiphenylmethane (DDM)-cured TGDDM. Dynamic mechanical analysis (DMA) shows that the DDM-cured TGDDM/SAN blends have two T _gs. A scanning electron microscopy (SEM) study revealed that all the DDM-cured TGDDM/SAN blends have a two-phase structure. The fracture toughness K _IC of the blends increased with SAN content and showed a maximum at 10 wt% SAN content, followed by a dramatic decrease for the cured blends containing 15 wt% SAN or more. The SEM investigation of the K _IC fracture surfaces indicated that the toughening effect of the SAN-modified epoxy resin was greatly dependent on the morphological structures.